TY - GEN

T1 - Balanced stable marriage

T2 - 16th International Symposium on Algorithms and Data Structures, WADS 2019

AU - Gupta, Sushmita

AU - Roy, Sanjukta

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Funding Information:
Keywords: Balanced Stable Marriage · Parameterized Complexity · Kernelization This work is supported by the European Research Council (ERC) via grant LOPPRE, reference no. 819416. Meirav Zehavi was supported by ISF (1176/18).
Publisher Copyright:
© Springer Nature Switzerland AG 2019.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Balanced Stable Marriage (BSM) is a central optimization version of the classic Stable Marriage (SM) problem. We study BSM from the viewpoint of Parameterized Complexity. Informally, the input of BSM consists of n men, n women, and an integer k. Each person a has a (sub)set of acceptable partners, A(a), who a ranks strictly; we use pa(b) to denote the position of b∈ A(a) in a’s preference list. The objective is to decide whether there exists a stable matching μ such that balance(formula presented). In SM, all stable matchings match the same set of agents, A* which can be computed in polynomial time. As balance (formula presented) for any stable matching μ, BSM is trivially fixed-parameter tractable (FPT) with respect to k. Thus, a natural question is whether BSM is FPT with respect to (formula presented). With this viewpoint in mind, we draw a line between tractability and intractability in relation to the target value. This line separates additional natural parameterizations higher/lower than ours (e.g., we automatically resolve the parameterization (formula presented). The two extreme stable matchings are the man-optimal μM and the woman-optimal μW. Let (formula presented), and (formula presented). In this work, we prove that BSM parameterized by (formula presented) admits (1) a kernel where the number of people is linear in t, and (2) a parameterized algorithm whose running time is single exponential in t.BSM parameterized by (formula presented) is W[1]-hard.

AB - Balanced Stable Marriage (BSM) is a central optimization version of the classic Stable Marriage (SM) problem. We study BSM from the viewpoint of Parameterized Complexity. Informally, the input of BSM consists of n men, n women, and an integer k. Each person a has a (sub)set of acceptable partners, A(a), who a ranks strictly; we use pa(b) to denote the position of b∈ A(a) in a’s preference list. The objective is to decide whether there exists a stable matching μ such that balance(formula presented). In SM, all stable matchings match the same set of agents, A* which can be computed in polynomial time. As balance (formula presented) for any stable matching μ, BSM is trivially fixed-parameter tractable (FPT) with respect to k. Thus, a natural question is whether BSM is FPT with respect to (formula presented). With this viewpoint in mind, we draw a line between tractability and intractability in relation to the target value. This line separates additional natural parameterizations higher/lower than ours (e.g., we automatically resolve the parameterization (formula presented). The two extreme stable matchings are the man-optimal μM and the woman-optimal μW. Let (formula presented), and (formula presented). In this work, we prove that BSM parameterized by (formula presented) admits (1) a kernel where the number of people is linear in t, and (2) a parameterized algorithm whose running time is single exponential in t.BSM parameterized by (formula presented) is W[1]-hard.

KW - Balanced stable marriage

KW - Kernelization

KW - Parameterized complexity

UR - http://www.scopus.com/inward/record.url?scp=85070594747&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-24766-9_31

DO - 10.1007/978-3-030-24766-9_31

M3 - Conference contribution

AN - SCOPUS:85070594747

SN - 9783030247652

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 423

EP - 437

BT - Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings

A2 - Friggstad, Zachary

A2 - Salavatipour, Mohammad R.

A2 - Sack, Jörg-Rüdiger

PB - Springer Verlag

Y2 - 5 August 2019 through 7 August 2019

ER -